Math Help Please, 10 Points to most helpful answer

http://i39.tinypic.com/347cpz6.png

Thanks to any and all help! :)

To find BC, you have to use tangent:opposite over adjacent

Then you have to set up an equation that reflects that tan 35 has to equal the opposite side divided by the adjacent side. In your problem, we are looking for the opposite side, so I will call that x, and the adjacent side is given, 13.

Our problem is this:

tangent 35=x/13

Now we can solve one we know what tan 35 is.


Now our equation is:

tan 35=x/13

We can now solve by isolating the x. We isolate the x by getting rid of the 13. What is the 13 doing to the x? it's splitting it up 13 times, so in order to find out what the x is, we have to multiply by 13 on both sides to get the x back.

tan 35=x/13
tan 35*13=x
9.102=x

So DC=9.102

And BC is double that, so it's 18.205 (it says nearest tenth, so 18.2 is the right answer)

Area is 0.5 * base * height

We know what the base is, it's BC which equals 18.205 (you have to re-round it up to get accurate answers)

We also know that the height is 13.

So let's multiply: 0.5 * 18.205 * 13 = 118.33 (rounded to the nearest tenth it is 118.3)

To find the perimeter, we need to know the hypotunuse of the half triangle:

We can do that using cosine:
cosine is adjacent over hypotunuse. Adjacent is 13, and hypotunuse is one we're looking for:

cosine 35=13/x

Now to sovlve for x we can cross multiply:

cosine 35/1=13/x

cross multiplication rules:

top left * bottom right has to equal top right * bottom left

top left: cosine 35
top right: 13
bottom left: 1
bottom right: x

top left * bottom right = top right * bottom left:
cosine 35 * x= 13 * 1
cosine 35 * x=13

We now divide cosine 35 on both sides to find x by itself:

(cosine 35 * x)/cosine 35=13/cosine 35